Answer: 544 adult tickets and 106 children's tickets were sold.
Explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of children's tickets that were sold.
Adult tickets cost $7.50 and children's ticket cost $4.50. The manager of the movie theater found that Saturday's sales were $3657. It means that
7.5x + 4.5y = 3657- - - - - - - - - - 1
He knew that a total of 650 tickets were sold Saturday. It means that
x + y = 650
Substituting x = 650 - y into equation 1, it becomes
7.5(650 - y) + 4.5y = 3657
4875 - 7.5y + 4.5y = 3657
- 7.5y + 4.5y = 3657 - 4875
3y = 1218
y = 318/3
y = 106
x = 650 - y = 650 - 106
x = 544